1. Circle Geometry – Determine the center, radius, and maximum distance of a point on a circle from the origin using its equation.
2. Exponential and Logarithmic Models – Use given models to find constants, solve equations, and work with exponential growth rates.
3. Cubic Equations – Analyze the intersections of cubic curves and solve for exact intersection points, given the equations.
4. Optimization and Differentiation – Differentiate expressions to find stationary points, and use further differentiation to confirm the nature of those points, including finding the minimum value.